Physicists often describe the fabric of the universe we
inhabit as four-dimensional spacetime, comprising three dimensions of
space and one of time. Yet whereas we spend our days passing freely
through space in any direction we wish (gravity and solid obstacles
permitting), time pushes us along, willingly or not, in a single,
predetermined direction: toward the future.

This is the arrow of time—life carries us from the past, through the present, and into the future. Back to the Future
plotlines notwithstanding, no one knows how to reverse the arrow—how to
move backward in time—and the logical paradoxes that would result from
such a trip into the past render it a thorny proposition at best.
(Thanks to a prediction of special relativity called time dilation,
travel into the distant future is relatively easy: just move really,
really fast.)

But I think the nuts and bolts of “ON THE ELECTRODYNAMICS OF MOVING
BODIES” aren't really considered carefully here, e.g...

“Sean Carroll Entangles Time and Entropy”, but is he correct
in doing so?

I'm not so sure about this, consider the idea, “time pushes
us along, willingly or not, in a single, predetermined direction: toward the
future.”, this might sound sensible, but consider what you actually observe if
you see, say, a car going along a street. In actual fact the car doesn’t actually
seem to head “into a future”, or leave a “temporal past” behind it.

Likewise, the idea “ life carries us from ‘the past’,
through the present, and into ‘the future’ ”, doesn’t actually seem to be
observed... do we actually have any scientific evidence at all that there is a
place or thing called “the past” behind us, or that we are heading not just
towards what is just in front of us, but also into a “future”?... doesn’t it
just actually appear that everything is just here, and you, I, and everything around
us is just moving and interacting?... do the patterns that form in our minds as
we observe things around us really count as scientific evidence to suggest
there also actually “is” a “past”?

If there actually isn’t a past or future, then isn’t the
idea of an arrow of time just, and only an “idea”?.

Quote “Thanks to a prediction of special relativity called
time dilation, travel into the distant future is relatively easy: just move
really, really fast.”... we might read this a lot, but have you actually
checked Special Relativity for yourself? i.e. “ON THE ELECTRODYNAMICS OF MOVING
BODIES”?

You should, "Electrodynamics"
"section 1 Kinematics “actually says...

If we wish to
describe the motion of a material point, we give the values of its co-ordinates
as functions of the time...

“The pointing of the
small hand of my watch to 7 and the arrival of the train are simultaneous
events.”

This seems perfectly acceptable, unless you realise that the
paper says we compare the co-ordinates ( location) of one thing to a thing
called “time”, But in fact the co-ordinates of one thing (a train) are only compared to the coordinates of another thing ( the
location of a rotating pointer).

(surely calling a rating pointer a “clock”, doesn’t prove
there is a thing called time that exists, or flows?)

So, logically, because SR doesn’t actuallygive any scientific evidence to suggest there
is a thing called “time”, that flows or passes, then surely what is described
as “time” dilation really just shows us that moving oscillators (e.g. those in
GPS satellites), “are” oscillating more slowly than ground based ones?

If there is no proof of a past, or of a future actually
existing, and if relativity provides no evidence to suggest a clock is anything
more than an oscillator, then that would (sadly) suggest fast moving things do
not “travel into ‘the future’ “, but are just “changing more slowly”.

Professor Carroll suggests that the un-reversable universal
entropy indicates the irreversible “arrow of time”, but, without proof that
moving things head into a future, or leave a past behind them, perhaps entropy
is just entropy..i.e. just eh fact and observation that a whole load of matter “is”
expanding outwards away from itself. And if so, perhaps entropy in no way
proves the “existence and one way flow of a thing called time”, it may just be
if we have extreme confirmation bias towards the idea there is a “one way
flowing thing called time”, we apply it to all we see, and try to make it fit?